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<head><title>intclMonIdeal -- Rees algebra</title>
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<div><h1>intclMonIdeal -- Rees algebra</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>intclMonIdeal(I)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, the leading monomials of the elements of the ideal are considered as generators of a monomial ideal whose Rees algebra is computed</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list containing one or two ideals</span></li>
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<div class="single"><h2>Description</h2>
<div>The exponent vectors of the leading monomials of the elements of <tt>I</tt> are considered as generators of a monomial ideal whose Rees algebra is computed. The function returns a list of ideals:<br/><br/><em>(i)</em> If the last ring variable is not used by the monomials, it is treated as the auxiliary variable of the Rees algebra. The function returns two ideals, the first containing the monomials generating the integral closure of the monomial ideal, the second containing the generators of the Rees algebra. <br/><br/><em>(ii)</em> If the last ring variable is used by the monomials, it returns only one ideal, namely the monomials generating the integral closure of the ideal.<table class="examples"><tr><td><pre>i1 : R=ZZ/37[x,y,t];</pre>
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<tr><td><pre>i2 : I=ideal(x^3, x^2*y, y^3, x*y^2);
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : intclMonIdeal(I)
3 2 2 3 3 2 2 3
o3 = {ideal (x , x y, x*y , y ), ideal (x, y, x t, x y*t, x*y t, y t)}
o3 : List</pre>
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<tr><td><pre>i4 : J=I+ideal(x*y^2*t^7);
o4 : Ideal of R</pre>
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<tr><td><pre>i5 : intclMonIdeal(J)
3 2 2 3
o5 = {ideal (x , x y, x*y , y )}
o5 : List</pre>
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<div class="waystouse"><h2>Ways to use <tt>intclMonIdeal</tt> :</h2>
<ul><li>intclMonIdeal(Ideal)</li>
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